US10285594B2 - Electric motor capable of reducing cogging torque - Google Patents
Electric motor capable of reducing cogging torque Download PDFInfo
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- US10285594B2 US10285594B2 US15/699,005 US201715699005A US10285594B2 US 10285594 B2 US10285594 B2 US 10285594B2 US 201715699005 A US201715699005 A US 201715699005A US 10285594 B2 US10285594 B2 US 10285594B2
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B5/00—Measuring for diagnostic purposes; Identification of persons
- A61B5/0059—Measuring for diagnostic purposes; Identification of persons using light, e.g. diagnosis by transillumination, diascopy, fluorescence
- A61B5/0062—Arrangements for scanning
- A61B5/0066—Optical coherence imaging
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
- A61B3/0016—Operational features thereof
- A61B3/0025—Operational features thereof characterised by electronic signal processing, e.g. eye models
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
- A61B3/10—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions
- A61B3/102—Objective types, i.e. instruments for examining the eyes independent of the patients' perceptions or reactions for optical coherence tomography [OCT]
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/02041—Interferometers characterised by particular imaging or detection techniques
- G01B9/02044—Imaging in the frequency domain, e.g. by using a spectrometer
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/02083—Interferometers characterised by particular signal processing and presentation
- G01B9/02084—Processing in the Fourier or frequency domain when not imaged in the frequency domain
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/0209—Low-coherence interferometers
- G01B9/02091—Tomographic interferometers, e.g. based on optical coherence
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/12—Stationary parts of the magnetic circuit
- H02K1/16—Stator cores with slots for windings
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/22—Rotating parts of the magnetic circuit
- H02K1/24—Rotor cores with salient poles ; Variable reluctance rotors
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/22—Rotating parts of the magnetic circuit
- H02K1/27—Rotor cores with permanent magnets
- H02K1/2706—Inner rotors
- H02K1/272—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis
- H02K1/274—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets
- H02K1/2753—Inner rotors the magnetisation axis of the magnets being perpendicular to the rotor axis the rotor consisting of two or more circumferentially positioned magnets the rotor consisting of magnets or groups of magnets arranged with alternating polarity
- H02K1/276—Magnets embedded in the magnetic core, e.g. interior permanent magnets [IPM]
- H02K1/2766—Magnets embedded in the magnetic core, e.g. interior permanent magnets [IPM] having a flux concentration effect
- H02K1/2773—Magnets embedded in the magnetic core, e.g. interior permanent magnets [IPM] having a flux concentration effect consisting of tangentially magnetized radial magnets
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B2562/00—Details of sensors; Constructional details of sensor housings or probes; Accessories for sensors
- A61B2562/02—Details of sensors specially adapted for in-vivo measurements
- A61B2562/0233—Special features of optical sensors or probes classified in A61B5/00
-
- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B2576/00—Medical imaging apparatus involving image processing or analysis
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K1/00—Details of the magnetic circuit
- H02K1/06—Details of the magnetic circuit characterised by the shape, form or construction
- H02K1/22—Rotating parts of the magnetic circuit
- H02K1/27—Rotor cores with permanent magnets
- H02K1/2706—Inner rotors
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K2213/00—Specific aspects, not otherwise provided for and not covered by codes H02K2201/00 - H02K2211/00
- H02K2213/03—Machines characterised by numerical values, ranges, mathematical expressions or similar information
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02K—DYNAMO-ELECTRIC MACHINES
- H02K29/00—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices
- H02K29/03—Motors or generators having non-mechanical commutating devices, e.g. discharge tubes or semiconductor devices with a magnetic circuit specially adapted for avoiding torque ripples or self-starting problems
Definitions
- the present invention relates to an electric motor capable of reducing cogging torque.
- a permanent magnet electric motor that includes a rotor having a permanent magnet
- magnetic coenergy fluctuates during rotation of the rotor, and therefore generates cogging torque that is torque pulsation.
- the cogging torque is preferably reduced because the cogging torque interferes with smooth rotation of the rotor to generate sound or vibration.
- electric motors as described in Japanese Laid-open Patent Publication No. 2003-023740 (JP2003-023740A) and Japanese Laid-open Patent Publication No. 11-164501 (JP11-164501A).
- a rotor of an electric motor described in JP2003-023740A includes a magnetic pole unit having a circular-arc outer peripheral surface bulged to an outside in a radial direction so that a waveform of a magnetic flux density generated from the rotor is a sine wave shape.
- Maximum outer diameter parts of the outer peripheral surface are arranged on both sides of a circumferential direction center (magnetic pole center) of the magnetic pole unit, and a concave part is formed in the circumferential direction center of the magnetic pole unit. This arrangement doubles the number of waveform peaks of cogging torque generated for each rotation of the rotor and reduces a magnitude of the cogging torque by half.
- JP11-164501A describes an electric motor in which an outer peripheral surface of a magnetic pole unit of a rotor is formed into a cylindrical shape around a rotary shaft of the rotor.
- This electric motor is configured such that a waveform of a magnetic flux density of the rotor is not a sine wave shape but a trapezoidal wave shape.
- the electric motor described in JP2003-023740A is configured to reduce the magnitude of cogging torque by half, by substantially doubling the number of magnetic poles, but is unable to adjust the magnitude of the cogging torque to an arbitrary magnitude.
- an electric motor includes a rotor including magnetic pole units, and a stator including slots facing an outer peripheral surface of the rotor.
- Each of the magnetic pole units is bulged to an outside in a radial direction so that a waveform of a magnetic flux density generated from the rotor is a sine wave shape.
- a concave part or convex part is formed at a central part in a circumferential direction of an outer peripheral surface in each of the magnetic pole units, and is small enough to prevent changing of a waveform period of cogging torque determined by a least common multiple of the number of slots and the number of magnetic poles of the rotor.
- FIG. 1 is a sectional view schematically illustrating an internal configuration of an electric motor according to an embodiment of the present invention
- FIG. 2A is an enlarged view illustrating a rotor illustrated in FIG. 1 ;
- FIG. 2B is an enlarged view illustrating a configuration of one pole of the rotor illustrated in FIG. 2A ;
- FIG. 3 is a diagram illustrating a waveform of a magnetic flux density when it is assumed that no slot opening is formed in an inner peripheral surface of a stator
- FIG. 4 is a diagram illustrating an example of magnetic flux lines in an electric motor
- FIG. 5 is a diagram illustrating a waveform of a magnetic flux density when a slot opening is formed in the inner peripheral surface of the stator
- FIG. 6 is an enlarged view illustrating an outer peripheral surface shape of the rotor constituting the electric motor according to the embodiment of the present invention.
- FIG. 7 is a diagram illustrating a change in waveform of cogging torque generated in the electric motor having the outer peripheral surface shape illustrated in FIG. 6 ;
- FIG. 8 is a diagram illustrating a change in waveform of cogging torque with changes of a maximum correction amount
- FIG. 9A is a diagram illustrating a rotor having a circular outer peripheral surface
- FIG. 9B is a diagram illustrating a waveform of a magnetic flux density generated from the rotor illustrated in FIG. 9A ;
- FIG. 10 is a diagram illustrating a change in waveform of cogging torque generated in the electric motor having the outer peripheral surface shape illustrated in FIG. 9A ;
- FIG. 11 is a diagram illustrating a modified example of the electric motor illustrated in FIG. 6 ;
- FIG. 12 is a diagram illustrating change in waveforms of cogging torque generated in the electric motor having an outer peripheral surface shape illustrated in FIG. 11 ;
- FIG. 13 is a diagram illustrating another modified example of the electric motor illustrated in FIG. 6 ;
- FIG. 14 is a diagram illustrating further modified example of the electric motor illustrated in FIG. 6 ;
- FIG. 15A is a diagram describing a method for setting of an outer peripheral surface shape of a rotor
- FIG. 15B is an enlarged view illustrating the outer peripheral surface shape of the rotor obtained by the method illustrated in FIG. 15A ;
- FIG. 16 is a diagram illustrating further modified example of the electric motor illustrated in FIG. 6 ;
- FIG. 17 is a diagram illustrating a change in waveform of cogging torque generated in the electric motor having an outer peripheral surface shape illustrated in FIG. 16 ;
- FIG. 18 is a diagram illustrating a modified example of the electric motor illustrated in FIG. 2A ;
- FIG. 19 is a diagram illustrating a modified example of the electric motor illustrated in FIG. 1 ;
- FIG. 20 is a diagram illustrating a change in waveform of cogging torque generated in the electric motor illustrated in FIG. 19 ;
- FIG. 21 is a diagram illustrating an example of magnetic flux lines in an electric motor according to further modified example of the electric motor illustrated in FIG. 1 .
- Predetermined space is formed between an outer peripheral surface 11 of the rotor 1 and an inner peripheral surface 21 of the stator 2 .
- slot openings 22 and teeth 23 are alternately formed in a circumferential direction.
- Slots 20 are formed on radial direction outsides of the slot openings 22 .
- a coil is received in each slot 20 .
- FIG. 2A is an enlarged view illustrating the rotor 1 .
- the eight permanent magnets 3 are radially arranged at equal intervals in a circumferential direction around a rotational center P 0 of the rotor 1 .
- Each yoke 10 is disposed between the permanent magnets 3 , 3 adjacent to each other in the circumferential direction, and eight magnetic poles (magnetic pole units) having the same shape are formed by the yokes 10 .
- the yokes 10 are configured by stacking a plurality of plate members in an axial direction and integrally fastening them via tie rods 5 .
- FIG. 2B is an enlarged view illustrating a configuration of a single yoke 10 , in other words, the rotor 1 of one pole, illustrated in FIG. 2A .
- a central angle of the rotor 1 is 45°.
- the rotor 1 has a line-symmetrical shape in the circumferential direction with respect to a reference line L 0 connecting the rotational center P 0 with a circumferential-direction center (magnetic pole center P 1 ) of an outer peripheral surface 11 of the yoke 10 by a straight line.
- the outer peripheral surface 11 of the yoke 10 is formed to bulge to an outside in a radial direction.
- a distance (rotor radius R) from the rotational center P 0 to the outer peripheral surface 11 of the yoke 10 is smaller as an angle ⁇ from the straight line L 0 is larger.
- the rotor radius R is maximum at a magnetic pole central part 12 in which ⁇ is 0°.
- An angle ⁇ from the reference line L 0 around the rotational center P 0 is also referred to as a mechanical angle.
- FIG. 3 is a diagram illustrating a waveform of a magnetic flux density B when it is assumed that no slot opening 22 is formed in an inner peripheral surface 21 of the stator 2 .
- This waveform is obtained by disposing a cylinder around the rotor 1 and measuring a magnetic flux between the rotor 1 and the cylinder in a static state of the rotor 1 .
- a horizontal axis indicates a mechanical angle of the rotor 1 while a vertical axis indicates a radial-direction component of the magnetic flux density B generated from the rotor 1 .
- One cycle of the waveform corresponds to a mechanical angle 45°.
- the rotor 1 has the outer peripheral surface 11 bulged to the radial direction outside.
- the magnetic flux density B generated from the rotor 1 is a sine wave shape, and the magnetic flux concentrates at the magnetic pole central part 12 (illustrated as an in FIG. 3 ).
- the real electric motor 100 includes the slot openings 22 formed in the inner peripheral surface 21 of the stator 2 .
- a difference is generated in magnetic permeability ⁇ between the slot openings 22 and the teeth 23 .
- magnetic permeability ⁇ of the teeth 23 composed of an electromagnetic steel sheet is generally larger by 1000 times or more than magnetic permeability ⁇ of the slot openings 22 determined by air and a coil (copper) in each slot 20 .
- the magnetic flux generated from the rotor 1 passes through the teeth 23 without passing through the slot openings 22 having high magnetic resistance.
- the magnetic flux is dense at the teeth 23 , thus generating a coarse/fine distribution of the magnetic flux density B in the circumferential direction.
- FIG. 5 is a diagram illustrating a waveform of the magnetic flux density B when slot openings 22 are formed in the inner peripheral surface 21 of the stator 2 .
- the sine wave shape is broken, and the magnetic flux density B approaches 0.
- the magnetic coenergy accordingly fluctuates to generate cogging torque.
- the cogging torque is preferably reduced because it interferes with smooth rotation of the rotor 1 to generate sound or vibration.
- the magnetic pole central part 12 of the rotor 1 (yoke 10 ) where the magnetic flux concentrates is configured as described below.
- FIG. 6 is an enlarged view illustrating an outer peripheral shape of the yoke 10 constituting the electric motor 100 according to the embodiment of the present invention.
- a horizontal axis indicates an angle from the reference line L 0 (illustrated in FIG. 2B ), in other words, a mechanical angle ⁇ , while a vertical axis indicates a distance from the rotational center P 0 to the outer peripheral surface 11 , in other words, a rotor radius R.
- the outer peripheral surface 11 (indicated by a solid line) is set by adding a correction amount ⁇ R in the radial direction using a mechanical angle ⁇ as a parameter to a reference surface 11 A (indicated by dotted line) using a mechanical angle ⁇ as a parameter.
- the reference surface 11 A is bulged to an outside in the radial direction so that the rotor radius R is maximum R 1 at the magnetic pole center P 1 of the mechanical angle 0°, and is formed into a circular arc shape as a whole.
- a waveform of the magnetic flux density B from the reference surface 11 A has a sine wave shape as illustrated in FIG. 3 when the presence of the slots 20 is ignored.
- a is a radius (stator inner diameter) of the inner peripheral surface 21 of the stator
- b is a minimum gap between the rotor 1 and the stator 2
- c is a coefficient.
- the mechanical angle ⁇ is set within a range of ⁇ 7.5° to 7.5°.
- d ⁇ sin(e ⁇ ) is a correction function indicating a correction amount ⁇ R
- d is a maximum correction amount
- e is a coefficient indicating characteristics of the correction function.
- the coefficient “e” is set so that e ⁇ can be respectively 180° and ⁇ 180° when the mechanical angle ⁇ is maximum and minimum. At this time, the correction amount ⁇ R is 0.
- a ratio b/a of the minimum gap “b” to the stator inner diameter “a” is, for example, about 1/10
- a ratio d/b of the maximum correction amount “d” to the minimum gap “b” is, for example, about 1/10.
- a ratio d/a of the maximum correction amount “d” to the stator inner diameter “a” is about 1/100
- the maximum correction amount “d” is considerably smaller than the stator inner diameter “a”.
- an absolute value of the maximum correction amount “d” is, for example, 0.1 mm or less. Visual checking of the presence of correction is consequently difficult. Checking can be performed by using a measuring device such as an optical projector. Strictly, the maximum correction amount “d” is set according to the size of the stator inner diameter “a” and the size of the minimum gap “b”. The maximum correction amount “d” is larger as the stator inner diameter “a” and the minimum gap “b” are larger. For example, the maximum correction amount “d” is within a range of 0.01 mm to 0.1 mm.
- FIG. 7 is a diagram illustrating a waveform of cogging torque.
- W 0 is a waveform of cogging torque when no correction is performed for the reference surface 11 A, in other words, when the rotor radius R is set along the dotted line illustrated in FIG. 6 .
- W 1 is a waveform of cogging torque when correction is performed for the reference surface 11 A, in other words, when the rotor radius R is set along the solid line illustrated in FIG. 6 .
- the cogging torque indicated by the waveform W 1 is smaller than that indicated by the waveform W 0 .
- a size of the cogging torque can be reduced by adding the correction amount ⁇ R to the rotor radius R of the reference surface 11 A to form the tiny concave part 15 at the magnetic pole central part 12 .
- FIG. 8 is a diagram illustrating a change in waveform of cogging torque with changes of the maximum correction amount “d”.
- Waveforms W 11 , W 12 , W 13 , W 14 , and W 15 are waveforms of cogging toque corresponding to maximum correction amounts d 1 , d 2 , d 3 , d 4 , and d 5 , respectively.
- the maximum correction amounts d 1 to d 5 are set in a relationship of d 1 ⁇ d 2 ⁇ d 3 ⁇ d 4 ⁇ d 5 . As illustrated in FIG.
- the cogging torque deviates from the waveform W 0 , and peak values of the cogging torque approach 0 (W 11 ⁇ W 12 ⁇ W 13 ).
- the maximum correction amount “d” increases more, waveforms (W 14 and W 15 ) of opposite phases are generated.
- the maximum correction amount “d” is very small (e.g., 0.1 mm or less).
- the present embodiment can provide the following operation effects.
- Each of the magnetic pole units (yokes 10 ) of the rotor 1 of the electric motor 100 is bulged to the radial direction outside so that the waveform of the magnetic flux density B generated from the rotor 1 is a sine wave shape (illustrated in FIG. 3 ), and the tiny concave part 15 (illustrated in FIG. 6 ) is formed at the central part in the circumferential direction (magnetic pole central part 12 ) of the outer peripheral surface 11 of the magnetic pole unit, which is small enough to prevent changing of the waveform cycle of the cogging torque determined by the least common multiple of the number of slots 20 and the number of magnetic poles of the rotor 1 .
- the cogging torque can be greatly reduced while keeping the waveform cycle of the cogging torque constant.
- the waveform cycle of the cogging torque is reduced to be about half.
- the magnitude of the cogging torque would be about half, reduction of the magnitude of the cogging torque of more than half is difficult.
- the magnitude of the cogging torque can be reduced to the utmost extent by appropriately adjusting the correction amount ⁇ R (maximum correction amount “d”) determining the concave part 15 .
- the aforementioned effect can be obtained in the case of the rotor 1 configured such that the rotor radius R of the reference surface 11 A is maximum at the magnetic pole central part 12 and the waveform of the magnetic flux density generated from the rotor 1 exhibits the sine wave shape.
- the waveform of the magnetic flux density generated from the rotor 1 exhibits the sine wave shape.
- FIG. 9A when an outer peripheral surface 111 of a rotor 101 has a circular shape, a waveform of a magnetic flux density B generated from the rotor 101 has a trapezoidal shape illustrated in FIG. 9B .
- FIG. 9A when an outer peripheral surface 111 of a rotor 101 has a circular shape, a waveform of a magnetic flux density B generated from the rotor 101 has a trapezoidal shape illustrated in FIG. 9B .
- FIG. 10 is a diagram illustrating a change in waveform of cogging torque when a correction amount ⁇ R is added to the reference surface 11 A as in the aforementioned case, with the outer peripheral surface 111 of the rotor 101 set as the reference surface 11 A.
- a waveform W 100 is a waveform of cogging torque when no correction is performed for the reference surface 11 A.
- Each of waveforms W 101 and W 102 is a waveform when correction is performed.
- the maximum correction amount “d” is set, for example, equal to or less than 0.1 mm, or about 1/100 of the stator inner diameter “a”, the correction amount ⁇ R is very small, and the magnitude of the cogging torque can be adjusted according to the maximum correction amount “d” without changing the cycle of the cogging torque.
- the maximum correction amount “d” is very small, a shape change of the magnetic pole unit is little, and only the magnitude of the cogging torque can be appropriately adjusted.
- the shape of the outer peripheral surface 11 of the magnetic pole unit in other words, the radius R from the rotor rotational center P 0 to the outer peripheral surface 11 , is set by adding the radial direction correction amount ⁇ R to the reference surface 11 A bulged to the radial direction outside so that the waveform of the magnetic flux density B generated from the rotor 1 exhibits the sine wave shape.
- shape setting of the outer peripheral surface 11 is easy.
- the concave part 15 is formed to have a smooth curve at the magnetic pole central part 12 .
- fluctuation of the magnetic coenergy caused by the presence of the concave part 15 can be suppressed.
- the correction amount ⁇ R is set based on the function using, as the parameter, the phase in which the circumferential-direction center of the magnetic pole unit is 0°, in other words, the function using, as the parameter, the mechanical angle ⁇ from the reference line L 0 passing through the magnetic pole center P 0 .
- setting of the correction amount ⁇ R changed with the increase of the mechanical angle ⁇ is easy.
- the correction amount ⁇ R is set by using the sine function.
- the concave part 15 with a smooth shape can be easily formed at the magnetic pole central part 12 .
- the cycle of the cogging torque is shortened to enable reduction of the magnitude of the cogging torque, but the number of slots 20 or magnets 3 increases.
- the cogging torque is reduced by forming the tiny concave part 15 at the magnetic pole central part 12 . This eliminates the necessity of increasing the least common multiple of the number of magnetic poles and the number of slots (in the embodiment, least common multiple is 24 ), and the number of slots 20 or magnets 3 can be reduced.
- the correction amount ⁇ R of the outer peripheral surface 11 of the magnetic pole unit in the radial direction is set by using the sine function.
- the correction amount ⁇ R can be set by using a cosine function or a hyperbolic cosine function.
- the rotor radius R of the reference surface 11 A may be given by the above formula (I)
- FIG. 11 is an enlarged view illustrating an outer peripheral shape of the yoke 10 obtained by the above formula (III).
- a dotted line in FIG. 11 is, as in the case illustrated in FIG. 6 , a rotor radius R of the reference surface 11 A.
- a tiny concave part 15 is formed at the magnetic pole central part 12 .
- a correction amount ⁇ R at the magnetic pole center P 1 is 0, and the minimum gap “b” is not changed before and after correction.
- FIG. 12 is a diagram illustrating a waveform of cogging torque when the outer peripheral surface 11 of the rotor 1 is configured as illustrated in FIG. 11 .
- W 0 and W 1 are respectively a waveform when no correction is performed for the reference surface 11 A (indicated by the dotted line in FIG. 11 ) and a waveform when correction is performed (indicated by the solid line in FIG. 11 ).
- the cogging torque indicated by the waveform W 1 is smaller than that indicated by the waveform W 0 .
- a magnitude of the cogging torque can be reduced by adding the correction amount ⁇ R to the rotor radius R of the reference surface 11 A to form the tiny concave part 15 at the magnetic pole central part 12 .
- FIG. 13 is a diagram illustrating an example where a tiny convex part 16 is formed.
- the rotor radius R is larger by a maximum correction amount “d” than that of the reference surface 11 A, and a minimum gap is accordingly smaller by a corresponding amount.
- the maximum correction amount “d” is very small, a changing amount of the minimum gap is small, causing no problem for gap setting for rotor rotation.
- the tiny convex part 16 is formed at the magnetic pole central part 12 , the minimum gap after correction may be matched with the minimum gap “b” before correction.
- the tiny concave part 15 or the tiny convex part 16 may be formed at the magnetic pole central part 12 by using a spline function.
- FIG. 14 is a diagram illustrating an example where a tiny concave part is formed at the magnetic pole central part 12 by using the spline function.
- the spline function is obtained by arbitrarily providing a sequence of points and sequentially connecting the points. For example, when the concave part 15 is formed by using the sine function, the sequence of points may be given along a sine curve and the points may be connected by the spline function.
- the tiny concave part 15 or the tiny convex part 16 may be formed at the magnetic pole central part 12 without using any of the aforementioned functions.
- the reference surface 11 A is rotated clockwise by only a predetermined angle ⁇ 1 (e.g., 10°) around the rotational center P 0 of the rotor 1 to obtain a first curved surface S 1 .
- the reference surface 11 A is rotated anticlockwise by only a predetermined angle ⁇ 1 to obtain a second curved surface S 2 .
- the first curved surface S 1 is symmetrically folded at the axis LO to obtain the second curved surface S 2 .
- the tiny concave part 15 or the tiny convex part 16 is formed at the magnetic pole central part 12 .
- “tiny” means a size enough to prevent changing of the waveform cycle of the cogging torque determined by the least common multiple of the number of slots 20 and the number of magnetic poles of the rotor 1 .
- size includes a depth of 0.1 mm or less for a concave part or a height of 0.1 mm or less for a convex part.
- Sizes of the concave part 15 and the convex part 16 are preferably set according to the outer diameter of the rotor 1 or the size of the minimum gap “b” instead of setting uniformly ignoring the size of the electric motor.
- the shape of the outer peripheral surface 11 of the rotor 1 is set based on the distance R from the rotational center P 0 of the rotor 1 .
- the shape (reference surface 11 a and correction amount ⁇ R) of the outer peripheral surface 11 of the rotor 1 may be set based on a distance R from a point P 2 offset from the rotational center P 0 .
- a reference point P 2 that is a reference for shape setting of the outer peripheral surface 11 may be set at a position shifted from the rotational center P 0 .
- FIG. 17 is a diagram illustrating a waveform of cogging torque with respect to the outer peripheral surface 11 illustrated in FIG. 16 .
- W 0 is a waveform when the reference surface 11 a is an outer peripheral surface 11
- W 1 is a waveform when the outer peripheral surface 11 is set by adding a correction amount ⁇ R to the reference surface 11 a to form the tiny concave part 15 at the magnetic pole central part 12 .
- the cogging torque can be reduced by forming the tiny concave part 15 at the magnetic pole central part 12 .
- the magnets 3 are radially arranged in the rotor 1 to form the magnetic pole units (illustrated in FIG. 2A ).
- the arrangement of the magnets 3 is not limited to this as long as the magnetic pole units are bulged to the outside in the radial direction so that the waveform of the magnetic flux density B generated from the rotor 1 is a sine wave shape.
- the magnets 3 may be buried along the circumferential direction of the rotor 1 to constitute an internal buried rotor 1 .
- the magnets may be stuck to a surface of the rotor 1 . In the example illustrated in FIG.
- an outer peripheral surface 11 of the rotor 1 is set by using a hyperbolic cosine function (cos h function).
- cos h function hyperbolic cosine function
- FIG. 20 is a diagram illustrating a waveform of cogging torque when the present invention is applied to the electric motor 100 A illustrated in FIG. 19 .
- waveforms W 0 and W 1 are respectively waveforms before and after tiny concave parts 15 are formed at the magnetic pole central parts 12 .
- the cogging torque can be reduced by forming the tiny concave parts 15 at the magnetic pole central parts 12 .
- FIG. 21 is a diagram illustrating magnetic flux lines in an electric motor 100 B with ten poles and twelve slots.
- the present invention can be similarly applied to the electric motor 100 B with ten poles and twelve slots.
- a generation number of times of cogging torque per rotation of the rotor 1 is determined by a least common multiple of the number of magnetic poles and the number of slots.
- the cogging torque can be reduced even without increasing the least common multiple.
- the least common multiple is preferably 100 or less.
- the embodiment can be arbitrarily combined with one or a plurality of modified examples.
- the concave or convex parts are formed at the central part in the circumferential direction of the outer peripheral surfaces of the magnetic pole units, and the concave or convex parts are small enough to prevent changing of the waveform cycle of the cogging torque determined by the least common multiple of the number of slots and the number of magnetic poles of the rotor.
- the magnitude of the cogging torque can be easily adjusted to an arbitrary magnitude.
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Abstract
Description
R=a−b/cos(Cθ) (I)
In the formula (I), “a” is a radius (stator inner diameter) of the inner
R=a−b/cos(cθ)+d×sin(eθ) (II)
In the formula (II), d×sin(eθ) is a correction function indicating a correction amount ΔR, “d” is a maximum correction amount, and “e” is a coefficient indicating characteristics of the correction function. For example, the coefficient “e” is set so that eθ can be respectively 180° and −180° when the mechanical angle θ is maximum and minimum. At this time, the correction amount ΔR is 0.
R=a−(b−d)/cos(cθ)+d/cos h(eθ) (III)
In the formula (III), 1/cos h(0)=1 is satisfied when θ=0. Accordingly, to match a minimum gap “b” after correction with a minimum gap “b” of the
R=a−b/cos(cθ)+d/cos h(eθ) (IV)
Claims (4)
R=a−b/cos(cθ)
ΔR=d sin(eθ),
R+ΔR=a−b/cos(cθ)+d sin(eθ),
R=a−b/cos(cθ)
ΔR=d/cos h(eθ)
R+ΔR=a−b/cos(cθ)+d/cos h(eθ)
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US15/699,005 US10285594B2 (en) | 2013-10-11 | 2017-09-08 | Electric motor capable of reducing cogging torque |
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JP2013-213736 | 2013-10-11 | ||
JP2013213736A JP5758966B2 (en) | 2013-10-11 | 2013-10-11 | Synchronous motor that can reduce cogging torque |
US14/509,170 US20150102700A1 (en) | 2013-10-11 | 2014-10-08 | Electric motor capable of reducing cogging torque |
US15/699,005 US10285594B2 (en) | 2013-10-11 | 2017-09-08 | Electric motor capable of reducing cogging torque |
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US14/509,170 Continuation US20150102700A1 (en) | 2013-10-11 | 2014-10-08 | Electric motor capable of reducing cogging torque |
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US20180020923A1 US20180020923A1 (en) | 2018-01-25 |
US10285594B2 true US10285594B2 (en) | 2019-05-14 |
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US15/699,005 Expired - Fee Related US10285594B2 (en) | 2013-10-11 | 2017-09-08 | Electric motor capable of reducing cogging torque |
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US14/509,170 Abandoned US20150102700A1 (en) | 2013-10-11 | 2014-10-08 | Electric motor capable of reducing cogging torque |
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US (2) | US20150102700A1 (en) |
JP (1) | JP5758966B2 (en) |
CN (2) | CN204179778U (en) |
DE (1) | DE102014114424A1 (en) |
Cited By (1)
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US20220037944A1 (en) * | 2020-07-31 | 2022-02-03 | GM Global Technology Operations LLC | Electric machine with non-magnetic lamination bridges |
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JP5758966B2 (en) | 2013-10-11 | 2015-08-05 | ファナック株式会社 | Synchronous motor that can reduce cogging torque |
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JP2019030166A (en) * | 2017-08-02 | 2019-02-21 | ミネベアミツミ株式会社 | motor |
CN107492960A (en) * | 2017-09-07 | 2017-12-19 | 日本电产凯宇汽车电器(江苏)有限公司 | A kind of cylindrical structure of the punching of permanent-magnetic synchronous motor rotor |
DE102017223650A1 (en) * | 2017-12-22 | 2019-06-27 | Robert Bosch Gmbh | Electric synchronous machine |
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FR3087962B1 (en) | 2018-10-29 | 2022-01-14 | Circor Ind | BRUSHLESS DIRECT CURRENT ELECTRIC MOTOR WITH REDUCED COGGING TORQUE AND METHOD OF MANUFACTURING THEREOF |
FR3088506B1 (en) | 2018-11-09 | 2021-06-25 | Circor Ind | PROCESS FOR REDUCING THE TORQUE PRODUCED BY ELECTRIC MOTORS OF THE BRUSHLESS TYPE USED SIMULTANEOUSLY |
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Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20220037944A1 (en) * | 2020-07-31 | 2022-02-03 | GM Global Technology Operations LLC | Electric machine with non-magnetic lamination bridges |
US11817748B2 (en) * | 2020-07-31 | 2023-11-14 | GM Global Technology Operations LLC | Electric machine with non-magnetic lamination bridges |
Also Published As
Publication number | Publication date |
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JP5758966B2 (en) | 2015-08-05 |
US20150102700A1 (en) | 2015-04-16 |
CN204179778U (en) | 2015-02-25 |
US20180020923A1 (en) | 2018-01-25 |
CN104578490A (en) | 2015-04-29 |
CN104578490B (en) | 2017-09-22 |
DE102014114424A1 (en) | 2015-04-16 |
JP2015077043A (en) | 2015-04-20 |
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